ABSTRACT
Corresponding to each symmetry, there is a conservation law with a characteristic conserving quantity which is invariant under that transformation. One of the aims of physical research is to search for symmetries and the corresponding observables that are invariant under certain classes of transformation. The Stone theorem ensures the existence of a Hermitian infinitesimal generator for an Abelian group of unitary transformation. The spatial translation operator is a specific example of this theorem and the momentum operator is the generator of spatial translation. This Galilean principle of relativity must be true in quantum mechanics as well. Time-reversal symmetry is a symmetry of the system under the transformation of time reversal.
